Theory:
Assuming it takes 30 seconds post game to 5 cap, you are talking about 98 seconds for winning (-5 per second, -10 for capping). 1:20 for game start + 30 seconds for cap + 1:38 seconds for winning.

3 minutes 28 seconds?

If you kill them as they spawn it would be even shorter...

Assuming 5 kills every 20 seconds. You'll be able to kill them 3 times for -30 so 3 minutes and 22 seconds.